Maximum product fuzzy relational inequalities with fuzzy constraints: an exact algorithm

Ghodousian, Amin; Pirhadi, Hossein

doi:10.22111/ijfs.2025.51165.9040

Document Type : Research Paper

Authors

Amin Ghodousian ¹
hossein pirhadi ²

¹ Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran.

² Faculty of Engineering Science, College of Engineering, University of Tehran.

https://doi.org/10.22111/ijfs.2025.51165.9040

Abstract

Fuzzy relational inequalities with fuzzy constraints (FRI-FC) represent a generalized form of fuzzy relational inequalities (FRI), in which fuzzy inequality replaces ordinary inequality in the constraints. With fuzzy constraints, we can obtain optimal points (called super-optima) that provide better solutions than those obtained by addressing similar problems with ordinary inequality constraints. In this paper, a linear objective function optimization problem with respect to a max-product FRI-FC problem is considered. Several optimization problems are equivalent to the primal problem, as it has been proven. The main problem is converted into a more simplified problem by means of some simplification operations based on the algebraic structure of the primary problem and its equivalent forms. As a result of a few mathematical manipulations, the main problem has been transformed into a linear optimization model. A super-optimum (which is better than the ordinary feasible optimal solution) is not only found by applying the proposed linearization method, but the best super-optimum is also identified for the main problem. A comparison is made between the current approach and our previous work, in addition to some well-known heuristic algorithms, by applying them to random test problems of different sizes and seeing how they compare to each other. Results demonstrate that the proposed method produces optimal solutions with admissible infeasibilities, while the linearization algorithm produces better solutions than other heuristic algorithms. In addition, the results demonstrate that heuristic algorithms could not escape from poor solutions in most cases.

Keywords

Main Subjects

Fuzzy modelling

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Maximum product fuzzy relational inequalities with fuzzy constraints: an exact algorithm

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Volume 23, Issue 1January and February 2026Pages 1-21

Volume 23, Issue 1
January and February 2026
Pages 1-21